How do I merge all of these objects into one, and only using one material and texture to apply colors using a UV color grid?
To join the objects, select them and then press CTRL + J.
but I imagine you only need a color grid material for all the objects in the scene and not really having them joined.

the easiest and fastest way to achieve this requires using and external addon.
http://renderhjs.net/textools/blender/

Once you have the addon installed you can just select all the objects in the scene (no need to join them) and assuming you already UV unwrap them, then in the UV window under the TexTools tab just press Checker Map. if you keep pressing Checker Map it will scroll between various grids